Noise Sensitivity of the Semidefinite Programs for Direct Data-Driven LQR
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909442084175872 |
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| author | Zeng, Xiong Bako, Laurent Ozay, Necmiye |
| author_facet | Zeng, Xiong Bako, Laurent Ozay, Necmiye |
| contents | In this paper, we study the noise sensitivity of the semidefinite program (SDP) proposed for direct data-driven infinite-horizon linear quadratic regulator (LQR) problem for discrete-time linear time-invariant systems. While this SDP is shown to find the true LQR controller in the noise-free setting, we show that it leads to a trivial solution with zero gain matrices when data is corrupted by noise, even when the noise is arbitrarily small. We then study a variant of the SDP that includes a robustness promoting regularization term and prove that regularization does not fully eliminate the sensitivity issue. In particular, the solution of the regularized SDP converges in probability also to a trivial solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19705 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noise Sensitivity of the Semidefinite Programs for Direct Data-Driven LQR Zeng, Xiong Bako, Laurent Ozay, Necmiye Optimization and Control Systems and Control In this paper, we study the noise sensitivity of the semidefinite program (SDP) proposed for direct data-driven infinite-horizon linear quadratic regulator (LQR) problem for discrete-time linear time-invariant systems. While this SDP is shown to find the true LQR controller in the noise-free setting, we show that it leads to a trivial solution with zero gain matrices when data is corrupted by noise, even when the noise is arbitrarily small. We then study a variant of the SDP that includes a robustness promoting regularization term and prove that regularization does not fully eliminate the sensitivity issue. In particular, the solution of the regularized SDP converges in probability also to a trivial solution. |
| title | Noise Sensitivity of the Semidefinite Programs for Direct Data-Driven LQR |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2412.19705 |